The House of Memories was built to hold graves from the Pokémon Tower when it was converted to the Kanto Radio Tower. There are many chambers within the building, but they cannot be accessed by anyone other than Mr. Fuji. There are no wild Pokémon or Trainers found within the House of Memories.
In HeartGold and SoulSilver, if the player stays in the House of Memories for too long and then talks to their walking Pokémon, a message saying that it either "appears somehow sad" or "is trembling with fear" appears, with the Pokémon eventually becoming angry at the player.
"May the Souls Of Pokémon Rest Easy"GSC, "May Pokémon Spirits Rest Easy"HGSS